In exterior calculus on smooth manifolds, the exterior derivative and wedge product are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial cochains play the role of discrete forms, the coboundary operator serves as the discrete exterior derivative, and the antisymmetrized cup product provides a discrete wedge product. In this paper we show that these discrete operations in DEC are natural with respect to abstract simplicial maps. A second contribution is a new combinatorial averaging interpretation of the discrete wedge product in DEC.

翻译：在光滑流形上的外微积分中，外导数与楔积相对于流形之间的光滑映射具有自然性，即这些运算与拉回映射可交换。在离散外微积分（DEC）中，单纯上链扮演离散形式（微分形式离散化）的角色，上边界算子充当离散外导数，而反对称化的杯积提供了离散楔积。本文证明了DEC中的这些离散运算相对于抽象单纯映射具有自然性。第二个贡献是提出了DEC中离散楔积的一种新的组合平均化解释。